Preheat an oven to 450F. Place the asparagus on a rimmed baking sheet large enough to hold them in a single layer. Brush the morels clean. If there is a lot of grit or other dirt lodged in their honeycomblike surface, you may need to dunk them briefly in cold water to free it; then pat dry with paper towels. If the morels are large, cut them crosswise into rings 1/4 inch wide. Leave small ones whole. Add the mushrooms to the baking sheet holding the asparagus. In a small saucepan over low heat, melt the butter. Add the shallots and saute for 1 minute to release their flavor. Drizzle the shallot butter evenly over the asparagus and morels. Scatter the tarragon over the top and season with salt and pepper. Using your hands, toss the asparagus and morels in the butter and tarragon until evenly coated, then spread them into a single layer again. Roast until the asparagus is lightly browned but still crisp and the morels are dark brown, about 10 minutes. Transfer the asparagus and morels to a serving platter and drizzle any pan juices over the top. Serve immediately.